Journal of Statistics: Advances in Theory and ApplicationsAuthor's: G. Pantsulaia and M. Kintsurashvili
Pages: [45] - [70]
Received Date: December 24, 2013; Revised February 11, 2014
Submitted by:
The notion of a Haar null set introduced by Christensen in 1973 and reintroduced in 1992 in the context of dynamical systems by Hunt, Sauer and Yorke, has been used, in the last two decades, in studying exceptional sets in diverse areas, including analysis, dynamic systems, group theory, and descriptive set theory. In the present paper, the notion of “prevalence†is used in studying the properties of some infinite sample statistics and in explaining why the null hypothesis is sometimes rejected for “almost every†infinite sample by some hypothesis testing of maximal reliability. To confirm that the conjectures of Jum Nunnally [17] and Jacob Cohen [5] fail for infinite samples, examples of the so called objective and strong objective infinite sample well-founded estimate of a useful signal in the linear one-dimensional stochastic model are constructed.
a linear one-dimensional stochastic model, null hypothesis, an objective infinite sample well-founded estimate, shy set, prevalence.
